Softening the color of the line gradually
Here are 3 ways to do it in Cycles Render:


With Mist: First go to your Render Layers menu > Passes > enable Mist. Now select your camera, go to the Object data menu > Display > enable Mist. Go to World menu > Mist Pass, and play with the length of the mist. Go to the Compositing, plug the Render Layer Mist output into the Factor of a Mix shader, and the Image into the top Image input of this Mix shader, then plug the output of the Mix Shader both in the input of the Viewer and the Compositer nodes. You can change the color of the mist with the bottom Image square of the Mix shader. You can add a Math node between the Render Layer and the Factor to change the mist intensity.
https://www.youtube.com/watch?v=CxNeMMZs_sM
With Volume Scatter: Create a box and increase its size until it contains your scene. Now in the Object menu > Display, choose Maximum Draw > Wire. Give it the following material: a simple Shader > Volume Scatter node plugged into the Volume of the Ouput. Lower down the node Density to something like 0.0X or 0.X. You can also add a Volume Absorption shader and mix it with the Volume Scatter in an Add Shader, so that the light is also absorbed.
https://www.youtube.com/watch?v=AXjE-t6dFZ8
With a Gradient Texture: Create a plane, assign it a material. Mix a Emission (white) and a Transparent in a Mix shader. In the Factor of this Mix shader, plug this node chain: Texture Coordinate that has its Object output plugged into a Mapping shader that has its Z Rotation 90°, that is plugged in a Gradient Texture node, that has its Color output plugged into a ColorRamp shader, that is plugged into the Mix Shader. Put this plane in front of your camera, behind your character, and play with the ColorRamp so that it fades your ground.